Is there a way to guarantee that your system tray icon is removed?
To add the system tray icon you do:
Shell_NotifyIcon(NIM_ADD, &m_tnd);
Hmm, you can always have an external monitor process call SendMessage with the WM_PAINT message to the system tray window (which you would have to do based on the class of the window). That should remove the icon which is no longer valid.